Multilayer optics with adjustable working wavelength

ABSTRACT

An electromagnetic reflector having a multilayer structure where the electromagnetic reflector is configured to reflect multiple electromagnetic frequencies.

BACKGROUND OF THE INVENTION

[0001] The present invention relates to an electromagnetic opticelement. More specifically the present invention relates to reflectivemultilayer x-ray optics having adjustable working wavelengths.

[0002] X-ray optics are used in many applications such as x-raydiffraction analysis and spectroscopy that require the directing,focusing, collimation, or monochromatizing of x-ray energy from an x-raysource. The family of x-ray optics or reflectors used in suchapplications presently include: total reflection mirrors having areflective surface coated with gold, copper, nickel, platinum, and othersimilar elements; crystal diffraction elements such as graphite; andmultilayer structures.

[0003] The reflective surfaces in the present invention are configuredas multilayer or graded-d multilayer x-ray reflective surfaces.Multilayer structures only reflect x-ray radiation when Bragg's equationis satisfied:

nλ=2dsin(θ)

[0004] where n = the order of reflection λ = wavelength of the incidentradiation d = layer-set spacing of a Bragg structure or the latticespacing of a crystal θ = angle of incidence

[0005] Multilayer or graded-d multilayer reflectors/mirrors are opticswhich utilize their inherent multilayer structure to reflect narrow bandor monochromatic x-ray radiation. The multilayer structure of thepresent invention comprises light element layers of relatively lowelectron density alternating with heavy element layers of relativelyhigh electron density, both of which define the d-spacing of themultilayer. The bandwidth of the reflected x-ray radiation can becustomized by manipulating the optical and multilayer parameters of thereflector. The d spacing may be changed depthwise to control thebandpass of the multilayer mirror. The d-spacing of a multilayer mirrorcan also be tailored through lateral grading in such a way that theBragg condition is satisfied at every point on a curved multilayerreflector.

[0006] Curved multilayer reflectors, including parabolic, elliptical,and other aspherically shaped reflectors must satisfy Bragg's law toreflect a certain specific x-ray wavelength (also referred to as energyor frequency). Bragg's law must be satisfied at every point on acurvature for a defined contour of such a reflecting mirror. Differentreflecting surfaces require different d-spacing to reflect a specificx-ray wavelength. This means the d-spacing should be matched with thecurvature of a reflector to satisfy Bragg's law such that the desiredx-ray wavelength will be reflected. Since Bragg's law must be satisfied,the incident angle and d-spacing are normally fixed and thus thereflected or working wavelength is fixed.

SUMMARY OF THE INVENTION

[0007] The present invention is a multilayer x-ray reflector/mirrorwhich may be used to reflect multiple x-ray wavelengths.

[0008] In a first embodiment, the multilayer structure has a laterallygraded d-spacing. The working (reflected) wavelength of the multilayerreflector may be changed by simply varying its curvature and thus theangle of incidence for an x-ray beam to satisfy Bragg's law.

[0009] In a second embodiment, an electromagnetic reflector has a fixedcurvature and a multilayer structure that has been configured to includea plurality of distinct d-spacings. The multilayer structure has alsobeen laterally graded such that the electromagnetic reflector mayreflect multiple x-ray wavelengths according to Bragg's law. Thus, thelateral grading of the d-spacings have been configured in conjunctionwith the curvature of the multilayer coating to reflect a plurality ofx-ray wavelengths.

[0010] In a third embodiment of the present invention an electromagneticreflector is formed with stripe-like multilayer coating sections. Eachof the coating sections has a fixed curvature and graded d-spacingtailored to reflect a specific wavelength. To change the workingwavelength of the reflector, the mirror or x-ray source need to be movedrelative to each other so that the appropriate coating section isaligned with the x-ray source.

BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The various advantages of the present invention will becomeapparent to those skilled in the art after reading the followingspecification and by reference to the drawings, in which:

[0012]FIG. 1 is a cross-sectional diagrammatic view of a multilayerBragg reflector;

[0013]FIG. 2 is a cross-sectional diagrammatic view of a multilayerreflector with a plurality of distinct d-spacings to reflect multiplex-ray wavelengths;

[0014]FIG. 3 is a cross-sectional view of a parabolically shapedreflector;

[0015]FIG. 4 is a cross-sectional view of an elliptically shapedreflector;

[0016]FIG. 5 is a magnified cross-sectional view taken within circle 5of FIG. 3;

[0017]FIG. 6 is a magnified cross-sectional view taken within circle 6of FIG. 3;

[0018]FIG. 7 is a magnified cross-sectional view taken within circle 7of FIG. 4;

[0019]FIG. 8 is a magnified cross-sectional view taken within circle 8of FIG. 4;

[0020]FIG. 9 is a diagrammatic view of the first embodiment of thereflector of the present invention illustrating its variable curvatureand ability to reflect different x-ray wavelengths;

[0021]FIG. 10 is a diagrammatic view of a bender used in the presentinvention;

[0022]FIG. 11 is a cross sectional view of the second embodiment of thereflector of the present invention having a fixed curvature that isconfigured to include a plurality of distinct d-spacings and laterallygraded such that it may reflect multiple x-ray wavelengths; and

[0023]FIG. 12 is a top view of the third embodiment of the reflector ofthe present invention with stripe-like sections having differentd-spacings such that the reflector can reflect a plurality of x-rayfrequencies.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0024]FIG. 1 is a cross-sectional diagrammatic view of a multilayerreflector 10. The multilayer reflector 10 is deposited on a substrate 12and comprises a plurality of layer sets with a thickness d. Each layerset 14 is made up of two separate layers of different materials; onewith a relatively high electron density and one with a relatively lowelectron density. In operation, x-ray radiation 13 is incident on themultilayer reflector 10 and narrow band or generally monochromaticradiation 16 is reflected according to Bragg's law.

[0025]FIG. 2 is a cross sectional diagram of a multilayer structure 18having a plurality of distinct d-spacings d1 and d2 varying in the depthdirection and defined as depth grading. The multilayer structure 18because of the distinct d-spacings d1 and d2 may reflect multiple x-raywavelengths (i.e. different groups of d-spacing to satisfy a discreterange of reflected wavelengths). In operation, polychromatic x-rayradiation 20 is incident on the surface of the multilayer structure 18and low energy x-rays 22 are reflected by the relatively thickerd-spacings d2 and high energy x-rays 24 are reflected by the relativelythinner d-spacings d1.

[0026]FIGS. 3 and 4 are cross-sectional diagrams of fixed curvaturemultilayer optics 26 and 28 which generally reflect only one x-raywavelength. FIG. 3 illustrates the parabolically shaped multilayer optic26 which collimates x-ray beams generated by an idealized point x-raysource 30 and FIG. 4 illustrates the elliptically shaped multilayeroptic 28 which focuses x-ray beams generated by an x-ray source 32 to afocal point 34. The curvature and d-spacing of optics 26 and 28 havebeen permanently configured to satisfy Bragg's law for a specificwavelength at every point on the surface of the optics 26 and 28.

[0027]FIGS. 5, 6, 7, and 8 are cross-sectional magnified views of themultilayer surfaces taken within circles 5, 6, 7, and 8 of FIGS. 3 and4. From these figures the variation in incident angle and the lateralgrading of the d-spacing in order to satisfy Bragg's law for a specificfrequency can be seen. In FIGS. 5 and 6 the parabolic optic 26 includesincident angle θ₁ and d-spacing d3 at one area of its surface andincident angle θ₂ and d-spacing d4 at another area. While theseparameters are different, the result is that these areas reflectgenerally the same x-ray wavelength following Bragg's law. Similarly, inFIGS. 7 and 8 the elliptical optic 28 includes incident angle θ₃ andd-spacing d5 at one area of its surface and incident angle θ₄ andd-spacing d6 at another area which reflect the same x-ray wavelength.The shortcomings with these type of fixed curvature reflectors is thatthey may only be used to reflect a single x-ray wavelength or narrowband.

[0028] As discussed previously, multilayer reflectors require differentd-spacing variations to reflect different x-ray wavelengths at the sameincident angle and the d-spacing should match the surface curvature(angle of incidence) to reflect x-rays according to Bragg's law. Thepresent invention provides electromagnetic reflectors which may be usedto reflect a plurality of x-ray wavelengths having substantially nooverlap.

[0029] A first embodiment of the present invention shown by FIG. 8comprises a multilayer reflector with variable curvature and a laterallygraded d-spacing. If a multilayer is a flat reflector with uniformd-spacing, the flat reflector can be rotated to reflect x-rays ofdifferent wavelengths, as the incidence angle will vary. If a multilayerhas a curved surface the d-spacing must be laterally graded to satisfyBragg's law at every point. Thus, the d-spacing or incidence angle maybe changed to vary the x-ray wavelength reflected from a multilayerreflector. The following discussion and equations will demonstrate thatfor certain x-ray wavelengths the laterally graded d-spacing of amultilayer reflector may remain constant while only the curvature isvaried and the curvature of a multilayer reflector may remain constantand have multiple graded d-spacings such that multiple x-ray wavelengthsmay be reflected by the multilayer reflector.

[0030] For parabolic, elliptical, and other aspherically shapedmultilayer optics, either the d-spacing variation of the multilayercoating or the curvature of the optics can be manipulated such that themultilayer optics reflect x-rays with different wavelengths. FollowingBragg's law the d-spacing is given by: $\begin{matrix}{d = \frac{\lambda}{2\sin \quad \theta}} & (1)\end{matrix}$

[0031] Where θ is the incident angle. It can be shown that the sin θ canbe written, at a very accurate approximation, as a product of a factor“C”(an arbitrary constant) and common form which is independent from thex-ray energy. The same d-spacing can be used for different wavelengthsby changing the factor C such that λ/C is a constant. Accordingly, sinθ, which is determined by the configuration of the reflection surface,can be maintained the same if d-spacing is proportionally changed withthe wavelength such that: $\begin{matrix}{{\sin \quad \theta} = \frac{\lambda}{2d}} & \left( {1b} \right)\end{matrix}$

[0032] is maintained constant for different wavelengths.

[0033] For a parabolic mirror the curvature of the reflecting surfacecan be written as:

y={square root}{square root over (2px)}  (2)

[0034] where p is the parabolic parameter. The accurate incident anglecan be given by the following formula:$\theta = {{\tan^{- 1}\left( \frac{\sqrt{2{px}}}{x - \frac{p}{2}} \right)} - {\tan^{- 1}\left( \sqrt{\frac{p}{2x}} \right.}}$

[0035] p generally is a number on the order of 0.1 and x is generally inthe range of several tens of millimeters to more than 100 millimeters.Due to the fact that θ is small where tan θ≈θ, the incident angle can bewritten as: $\begin{matrix}{\theta = {\sqrt{p}\frac{1}{\sqrt{2x}}}} & (3)\end{matrix}$

[0036] Using small angle approximation, d-spacing is determined by:$\begin{matrix}{d = {\frac{\lambda}{\sqrt{p}}\sqrt{\frac{x}{2}}}} & (4)\end{matrix}$

[0037] From the equations shown above it can be shown that d-spacing canbe maintained for different reflected wavelengths by altering thecurvature or parabolic parameter (ρ) of a parabolic shaped multilayerreflector.

[0038] For an elliptical mirror, the reflection surface is described bythe equation: $\begin{matrix}{{\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}} = 1} & (5)\end{matrix}$

[0039] Where x and y are points in a Cartesian coordinate system and ais the major radius of the ellipse and b is the minor radius of theellipse. The incident angle is given by the equation:$\theta = {{\tan^{- 1}\left( \frac{{b/a}\sqrt{a^{2} - x^{2}}}{x + c} \right)} - {\tan^{- 1}\left( \frac{{- 2}{bx}}{{a\sqrt{a^{2}}} - x^{2}} \right.}}$

[0040] where c is defined by the equation:

c={square root}{square root over (a² −b ²)}

[0041] For an x-ray elliptical mirror, the minor radius is much smallerthan the major radius. Using small angle approximation, the aboveequation can be written as:$\theta \approx {\frac{q\sqrt{a^{2} - x^{2}}}{x + {a\sqrt{1 - q^{2}}}} - \frac{{- 2}{qx}}{\sqrt{a^{2} - x^{2}}}}$

[0042] where q=b/a. Therefore the d-spacing is given by the equation:$\begin{matrix}{d = {\frac{\lambda}{q}\frac{1}{2\left( {\frac{\sqrt{a^{2} - x^{2}}}{x + a} + \frac{2x}{\sqrt{a^{2} - x^{2}}}} \right)}}} & (6)\end{matrix}$

[0043] From the above formula, it can be shown that the d-spacing andfocal position can be maintained by just changing the minor radius b.

[0044] Furthermore, we determine how d-spacing is defined as well as thewavelength dependency on d-spacing for a multilayer reflector. Thed-spacing used in this application is defined by using first orderBragg's law (n=1), since multilayers generally operate under first orderreflection. The “real d-spacing”, or the “geometric d-spacing isdifferent from the “first order Bragg d-spacing” due to the effects ofrefraction in the multilayer structure. In most applications amultilayer optic is used as a first order Bragg reflector. This is thereason that “d-spacing” is commonly defined and measured by the firstorder Bragg's law. Such defined d-spacing is the same for differentwavelengths as shown in the following discussion.

[0045] The “real d-spacing” d_(r) is given by the following equation:$\begin{matrix}{d_{r} = {d\left( {1 - \frac{\delta}{\sin^{2}\theta}} \right)}} & (7)\end{matrix}$

[0046] where δ is the optical index decrement. Therefore, higher ordermeasurement gives a d-spacing closer to the “real d-spacing”. However,the optical index is proportional to the square of the wavelength and sois sin²θ. Therefore, the above equation becomes:

d ^(r) =d(1−Ad ²)  (8)

[0047] where A is a constant not dependent on energy. This means thatthe “first order d-spacing” is the same for different wavelengths andthe d-spacing measured by different wavelengths is the same.

[0048] Referring to FIG. 9 and the first embodiment of the presentinvention, a variable curvature multilayer reflector 36, is shown in twopositions 38 and 40 having two different curvatures defined by theellipses 33 and 35 and reflecting different x-ray wavelengths 39 and 41to a focal point 31. A similar scheme may be configured for paraboliccollimating mirrors which conform to two different parabolas. Thereflector 36 has more curvature at position 38 then at position 40. Theincreased curvature will allow the reflector to reflect larger x-raywavelengths at position 38 then at position 40. The reflector atposition 40 is modified with less curvature then at position 38 and willreflect shorter x-ray wavelengths. The curvature of the reflector 36 isexaggerated in FIG. 9 to help illustrate the curvature at the alternatepositions 38 and 40.

[0049] For a variable curvature parabolic mirror from Formula 4:

λ/{square root}{square root over (p)}=C

[0050] for all the wavelengths. Therefore the parabolic parameter mustchange in the following way: $\begin{matrix}{p = \frac{\lambda^{2}}{C^{2}}} & (9)\end{matrix}$

[0051] For an elliptical mirror, according to formula 6, the minorradius b must change as: $\begin{matrix}{b = \frac{\lambda \quad a}{C}} & (10)\end{matrix}$

[0052] Thus, the manipulation of the parabolic parameter p of theparabolic reflector and the minor radius b of the elliptical reflectormay be adjusted to vary the wavelength of the reflected x-rays.

[0053] A four point bender 42 is shown in FIG. 10 having precisionactuators 44 a and 44 b which will vary the curvature of the reflector36. Posts 43 are fixed while members 45 are actuated to alter thecurvature of the reflector 36. The bender 42 will vary the parabolicparameter p of a parabolically shaped multilayer reflector and the minorradius b of an elliptically shaped multilayer reflector as detailedabove.

[0054] In a second embodiment of the present invention shown in FIG. 11,a multilayer reflector 46 of fixed curvature, with a plurality ofdistinct d-spacings d7 and d8, is configured to reflect multiple x-raywavelengths. Each d-spacing d7 and d8 will satisfy Bragg's law for aspecific x-ray wavelength. The relatively larger d-spacing d8 willreflect longer wavelengths and the relatively shorter d-spacing d7 willreflect shorter wavelengths. The reflected wavelengths will havesubstantially no overlap. Since the absorption for lower energy (longerwavelength) x-rays is stronger, the reflection layer d8 for the lowerenergy x-rays should be the top layers on the reflector 46. As can beseen in the drawing, the d-spacings d7 and d8 are laterally graded incooperation with the curvature of the reflector 46 to satisfy Bragg'slaw for a plurality of specific x-ray wavelengths. In alternateembodiments of the present invention additional groups of d-spacings maybe used limited only by the dimensions and structure of the reflector46.

[0055] In a third embodiment of the present invention seen in FIG. 12(an overhead or top view) a multilayer reflector 48 having stripe likesections 50 with different d-spacings is shown. Each stripe 50 has ad-spacing configured to reflect specific x-ray wavelengths. An x-raysource 52 needs only to be translated relative to the stripe likesections 50 of the reflector 48 to change the wavelength of the x-raysreflected from the reflector 48. The preferred method of translation isto fix the position of the x-ray source 52 while translating thereflector 48.

[0056] It is to be understood that the invention is not limited to theexact construction illustrated and described above, but that variouschanges and modifications may be made without departing from the spiritand scope of the invention as defined in the following claims.

I claim:
 1. An electromagnetic reflector comprising: a multilayer structure having a d-spacing, wherein said multilayer structure's curvature may be varied by a movement apparatus to reflect multiple electromagnetic frequencies.
 2. The electromagnetic reflector of claim 1, wherein said multilayer is deposited on a substrate.
 3. The electromagnetic reflector of claim 1, wherein said d-spacing is laterally graded.
 4. The electromagnetic reflector of claim 1, wherein said electromagnetic frequencies are x-ray frequencies.
 5. The electromagnetic reflector of claim 1, wherein said movement apparatus is a bender which alters the curvature of said multilayer structure.
 6. The electromagnetic reflector of claim 5, wherein said bender is a four point bender.
 7. An x-ray reflector comprising: a substrate; a multilayer structure coupled to said substrate, wherein said multilayer structure is of fixed curvature; and said multilayer structure having at least two distinct groups of d-spacing, wherein the x-ray reflector may reflect a plurality of x-ray frequencies.
 8. The x-ray reflector of claim 7, wherein the thicker of said groups of d-spacing is mounted on the top of said multilayer structure.
 9. The x-ray reflector of claim 7, wherein the mutlilayer is laterally graded.
 10. The x-ray reflector of claim 7, wherein the multilayer is deposited on said substrate.
 11. An electromagnetic optic comprising: a multilayer surface, said multilayer surface having a variable curvature, whereby said multilayer surface will reflect different wavelengths of electromagnetic energy based on said variable curvature.
 12. The electromagnetic optic of claim 11, wherein said multilayer is laterally graded.
 13. The electromagnetic optic of claim 11, wherein said electromagnetic energy is x-rays.
 14. The electromagnetic optic of claim 11 further including a bender to alter the curvature of said multilayer surface.
 15. A variable curvature x-ray reflector comprising: a substrate; a multilayer surface coupled to said substrate, wherein said multilayer is laterally graded; and wherein as said curvature of the x-ray reflector is varied the frequency of reflected electromagnetic radiation is also varied.
 16. The variable curvature x-ray reflector of claim 15, wherein the variable curvature x-ray reflector is shaped as a parabolic curve and the p factor is varied to change the curvature of the variable curvature x-ray reflector.
 17. The variable curvature x-ray reflector of claim 15, wherein the variable curvature x-ray reflector is shaped as an elliptical curve and the minor radius is varied to change the curvature of the variable curvature x-ray reflector.
 18. A method of reflecting multiple electromagnetic frequencies with a multilayer reflector comprising: generating electromagnetic energy; directing said electromagnetic energy at the multilayer reflector; and adjusting the curvature of the multilayer reflector to reflect said electromagnetic energy in accordance with Bragg's law.
 19. An x-ray reflector comprising a plurality of stripe-like multilayer sections arranged side by side, wherein each said multilayer section has a d-spacing configured to reflect a different x-ray frequency.
 20. The x-ray reflector of claim 19, wherein said multilayer sections are configured with an elliptical surface.
 21. The x-ray reflector of claim 19, wherein said multilayer sections are configured with a parabolic surface. 